Group Importances#

In this notebook we show how to compute and interpret Overall Importances shown in InterpretML’s Global Explanations for EBMs. We also show how to compute importances of a group of features or terms.

Throughout the notebook we use term to denote both single features and interactions (pairs).

This notebook can be found in our examples folder on GitHub.

# install interpret if not already installed
try:
    import interpret
except ModuleNotFoundError:
    !pip install --quiet interpret pandas scikit-learn

Train an Explainable Boosting Machine (EBM) for a regression task

Let’s use the Boston dataset as a reference and train an EBM.

import numpy as np
import pandas as pd
from sklearn.datasets import load_diabetes
from interpret.glassbox import ExplainableBoostingRegressor

from interpret import set_visualize_provider
from interpret.provider import InlineProvider
set_visualize_provider(InlineProvider())

X, y = load_diabetes(return_X_y=True, as_frame=True)

ebm = ExplainableBoostingRegressor()
ebm.fit(X, y) 

ExplainableBoostingRegressor()
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Explain the Model

EBMs provide two different kinds of explanations: global explanations about the overall model behavior and local explanations about individual predictions from the model.

Global Explanation

Global Explanations are useful for understanding what a model finds important, as well as identifying potential flaws in its decision making or the training data. Let’s start by computing and displaying a global explanation:

from interpret import show
show(ebm.explain_global(name='EBM'))

The overall importance for each term is calculated as the average absolute contribution (score) a term (feature or pair) makes when predicting across the training dataset. This way of measuring term importance tends to favor terms which, on average, have large impact on predictions for many cases. The overall importance is not a measure of positive/negative – it is a measure of how important each term is in the scores. For regression, these scores are represented in the same units as the y-axis of the feature graphs. For classification, the scores would be in logits.

Going beyond overall term importances, because EBMs are additive models we can measure exactly how each term contributes to a prediction. Let’s take a look at the graph of the term, bp, by selecting it in the drop-down menu.

Global Explanation - LSTAT

The way to interpret this is that if a new datapoint came in with bp = 0.1, the model adds about +33.1 to the final prediction. However, for a different datapoint with bp = 0.13, the model would now add approx. +36.7 to the prediction.

To make individual predictions, the model uses each term graph as a look up table, notes the contribution per term, and sums them together with the learned intercept to make a prediction. In regression, the intercept is the mean target (label) of the training set, and each term adds or subtracts to this mean. In classification, the intercept reflects the base rate of the positive class on a log scale. The gray above and below the graph shows the confidence of the model in that region of the graph.

Local Explanations

We can see the full breakdown of a prediction on a single sample with Local Explanations. Here’s how to compute the prediction breakdown for the first sample in our dataset:

from interpret import show
show(ebm.explain_local(X[:1], y[:1]), 0)

Let’s take a look at the prediction by selecting it in the drop-down menu.

Local Explanation

The model prediction is 188.50. We can see that the intercept adds about +151.9, bp subtracts about 0.02, and age adds about 0.04. If we repeat this process for all the terms, we’ll arrive exactly at the model prediction of 188.50.

Viewing _all_ term importances

Due to space limitations in our graphs, the term importance summary only shows the top 15 terms. To view the overall importances of all terms of a trained EBM - the scores shown in the global explanation summary - we use term_importances():

importances = ebm.term_importances()
names = ebm.term_names_

for (term_name, importance) in zip(names, importances):
    print(f"Term {term_name} importance: {importance}")

Term age importance: 3.354518859311848
Term sex importance: 7.792443414262308
Term bmi importance: 16.885314529174654
Term bp importance: 10.481809867089009
Term s1 importance: 0.9054666470912439
Term s2 importance: 2.8693080927690966
Term s3 importance: 7.027393843851522
Term s4 importance: 6.381393860800107
Term s5 importance: 16.150868538758225
Term s6 importance: 5.267113181662991
Term age & bmi importance: 0.8033975070327222
Term age & s5 importance: 1.2900468091599138
Term bmi & bp importance: 1.0730811945988519
Term bmi & s2 importance: 1.003800477506845
Term bmi & s4 importance: 1.4206254640868787
Term bmi & s5 importance: 0.8677487601101491
Term bmi & s6 importance: 0.9648195605069537
Term s1 & s5 importance: 1.4304133551178637
Term s5 & s6 importance: 2.0696633483383677

Note that mean absolute contribution isn’t the only way of calculating term importances. Another metric our package provides is the min_max option, which computes the difference between the max (the highest score on the graph) and min (the lowest score on the graph) values for each term. Term importance measured with min_max is a measure of the maximum impact a term can have, even though it might have this amount of impact on very few cases, whereas avg_weight(the default parameter) is a measure of typical (average) contribution of a term across all cases.

importances = ebm.term_importances("min_max")
names = ebm.term_names_

for (term, importance) in zip(names, importances):
    print(f"Term {term} importance: {importance}")

Term age importance: 13.903756152607327
Term sex importance: 15.647681315489173
Term bmi importance: 92.02609158409899
Term bp importance: 64.23969384023191
Term s1 importance: 7.906096141303943
Term s2 importance: 21.004987765103373
Term s3 importance: 52.27759118120582
Term s4 importance: 29.917191279702813
Term s5 importance: 58.185055742113946
Term s6 importance: 37.98831763947467
Term age & bmi importance: 11.05865403539901
Term age & s5 importance: 7.341049123257411
Term bmi & bp importance: 13.875548946860382
Term bmi & s2 importance: 12.246608831779842
Term bmi & s4 importance: 6.848205296564537
Term bmi & s5 importance: 7.716274088235214
Term bmi & s6 importance: 8.023103480296577
Term s1 & s5 importance: 15.151989801134004
Term s5 & s6 importance: 21.839655466499472

Feature/Term Group Importances

We provide utility functions to compute the importances of groups of features or terms and, optionally, append these importances to the global feature attribution bar graph. Note that shape function graphs are not generated for groups of features/terms, just their overall importance is shown on the Summary.

Grouping terms and then calculating and displaying their importance does not change the model and the predictions it makes in any way – group importances are just a method for computing the importance of groups of terms in addition to the importances of individual terms that are already calculated. As you’ll see in the examples below, it’s OK for features/terms to overlap in different groups.

Computing group importances

Let’s use the Adult dataset and train an EBM for a classification task.

import numpy as np
import pandas as pd
from interpret.glassbox import ExplainableBoostingClassifier

df = pd.read_csv(
    "https://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data",
    header=None)
df.columns = [
    "Age", "WorkClass", "fnlwgt", "Education", "EducationNum",
    "MaritalStatus", "Occupation", "Relationship", "Race", "Gender",
    "CapitalGain", "CapitalLoss", "HoursPerWeek", "NativeCountry", "Income"
]
X = df.iloc[:, :-1]
y = df.iloc[:, -1]

adult_ebm = ExplainableBoostingClassifier()
adult_ebm.fit(X, y)

ExplainableBoostingClassifier()
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We then create a list of terms – single features or interactions – as our group and compute its importance:

from interpret.glassbox._ebm._research import *

social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
importance = compute_group_importance(social_feature_group, adult_ebm, X)
print(f"Group: {social_feature_group} - Importance: {importance}")

Group: ['MaritalStatus', 'Relationship', 'Race', 'Gender', 'NativeCountry'] - Importance: 1.2912109901324624

In this example we create a group with five terms and compute its importance. Similar to single feature importances, we interpret this score as the average absolute contribution this group of terms makes when predicting across the training dataset. Note that for each prediction, the contribution of each term in the group will be added before taking the absolute value.

We also have the option to create a global explanation containing the group importance or append it to an existing explanation:

my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
show(my_global_exp)

The importance of social_feature_group is about 1.30, which is higher than the importance of any individual feature/term:

Global Explanation - Social Feature Group

We could make this type of comparison between different groups too:

education_feature_group = ["Education", "EducationNum"]
relationship_feature_group = ["MaritalStatus", "Relationship"]
social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
my_global_exp = append_group_importance(education_feature_group, adult_ebm, X, global_exp=my_global_exp)
my_global_exp = append_group_importance(relationship_feature_group, adult_ebm, X, global_exp=my_global_exp)
show(my_global_exp)

The importance of education_feature_group is about 0.52, higher than each of its individual terms but smaller than some individual terms such as Age. Remember, creating groups of features/terms does not, in any way, change the model and its predictions, it only allows you to estimate the importance of these groups.

This graph, for example, suggests that features related to relationships are more important than features reated to education.

Global Explanation - Education Group

We can also compare a group we are interested in (e.g. social_feature_group) with a group of all other reamining terms.

social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
all_other_terms = [term for term in adult_ebm.term_names_ if term not in social_feature_group]

my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
my_global_exp = append_group_importance(all_other_terms, adult_ebm, X, group_name="all_other_terms", global_exp=my_global_exp)
show(my_global_exp)

Note that all_other_terms has the highest importance score, followed by social_feature_group.

Global Explanation - All Other Group

It’s even possible to create a group with all terms.

all_terms_group = [term for term in adult_ebm.term_names_]
mew_global_exp = append_group_importance(all_terms_group, adult_ebm, X, group_name="all_terms")
show(mew_global_exp)

Finally, we also expose a function to compute the importances of a group of terms as well as all the model’s original terms.

my_dict = get_group_and_individual_importances([social_feature_group, education_feature_group], adult_ebm, X)
for key in my_dict:
    print(f"Term: {key} - Importance: {my_dict[key]}")

Term: MaritalStatus, Relationship, Race, Gender, NativeCountry - Importance: 1.2912109901324624
Term: Age - Importance: 0.8182080583906379
Term: CapitalGain - Importance: 0.6718022055499319
Term: Relationship - Importance: 0.6009464219074515
Term: MaritalStatus - Importance: 0.548352541090868
Term: Education, EducationNum - Importance: 0.5228062448815415
Term: EducationNum - Importance: 0.4024014798924508
Term: Occupation - Importance: 0.37199765713750416
Term: Gender - Importance: 0.303576490779585
Term: HoursPerWeek - Importance: 0.29377319486986797
Term: CapitalLoss - Importance: 0.1696300865245867
Term: Education - Importance: 0.15781649312344925
Term: fnlwgt - Importance: 0.11652607734497236
Term: WorkClass - Importance: 0.09058168201221616
Term: Race - Importance: 0.0658366455036571
Term: NativeCountry - Importance: 0.062414796208145454
Term: Age & HoursPerWeek - Importance: 0.06094949527714537
Term: MaritalStatus & HoursPerWeek - Importance: 0.04972618390555662
Term: Relationship & HoursPerWeek - Importance: 0.04308241145428646
Term: EducationNum & MaritalStatus - Importance: 0.03656207669361272
Term: Age & EducationNum - Importance: 0.036049758872003075
Term: fnlwgt & Education - Importance: 0.032094435175994224
Term: Age & fnlwgt - Importance: 0.030712769881581593
Term: Gender & HoursPerWeek - Importance: 0.025960827984811634
Term: Age & Race - Importance: 0.025000110953315655
Term: Age & Relationship - Importance: 0.020796943779334068
Term: MaritalStatus & Gender - Importance: 0.019515723133531764
Term: WorkClass & Relationship - Importance: 0.01726050499720248
Term: WorkClass & Race - Importance: 0.007914950536676572